JP6532330B2 - Correction method of image forming apparatus - Google Patents

Description

  The present invention relates to a correction method of an image forming apparatus such as a digital copying machine, a multi-function machine, a laser printer, and distortion and density unevenness in image formation of a two-dimensional image.

  In an electrophotographic image forming apparatus such as a laser printer and a copier, it is generally known to form a latent image on a photosensitive member using an optical scanning device for scanning a laser beam. In a laser scanning type optical scanning device, a collimated laser beam is deflected by a rotating polygon mirror using a collimator lens, and the deflected laser beam is imaged on a photosensitive member using a long fθ lens. Let In addition, there is a multi-beam scanning method in which a multi-beam light source having a plurality of light emitting elements is included in one package, and a plurality of laser beams are scanned simultaneously.

  On the other hand, in order to form a good image free from uneven density and banding, it is desirable that the pitches between scanning lines of each laser beam be equal on the photosensitive member. However, due to the following factors, pitch variation between scan lines occurs. For example, the variation in pitch between scan lines is caused by the variation in surface velocity of the photosensitive member, the variation in rotational velocity of the rotating polygon mirror, and the like. The variation in pitch between scanning lines is also caused by the variation in the angle of the mirror surface of the rotating polygon mirror with respect to the rotation axis of the rotating polygon mirror and the variation in the distance between the light emission points arranged in the multibeam laser chip. There has been proposed a technique for correcting banding by controlling the exposure amount of the optical scanning device against uneven density and banding generated due to such factors. For example, in Patent Document 1, a beam position detection unit in the sub-scanning direction is provided in the vicinity of the photosensitive member, and the exposure amount of the light scanning device is adjusted based on scanning pitch information obtained from the detected beam position to make banding inconspicuous. Configuration is described.

JP, 2012-098622, A

  In a scanning optical system that scans a laser beam with a rotating polygon mirror, the mirror surface of the rotating polygon mirror falls (hereinafter referred to as a surface tilt of the rotating polygon mirror) for each position in the main scanning direction of the laser beam. Results in different amounts of). FIG. 16 shows the respective positions of the scanning position of the 2000th line from the image head scanned by the mirror surface 1 of the rotary polygon mirror and the scanning position of the 4000th line from the image head scanned by the mirror surface 2. . Also, the deviations of the scanning position of the 6000th line from the top of the image scanned by the mirror surface 3 of the rotary polygon mirror and the scanning position of the 8000th line from the top of the image scanned by the mirror surface 4 are shown. Further, the situation of deviation of the scanning position of the 10000th line from the head of the image scanned by the mirror surface 5 of the rotary polygon mirror is shown. In FIG. 16, depending on the position in the main scanning direction, the scanning position of the scanning line indicated by the solid line is deviated in the leading direction or deviated in the opposite direction to the leading direction with respect to the ideal position indicated by the broken line. Further, the deviation amount of the scanning position of the scanning line with respect to the ideal position also varies among the scanning lines in the sub-scanning direction. As described above, the influence of the surface tilt of the rotary polygon mirror is different for each scanning line in the sub scanning direction of the laser light and each position in the main scanning direction, and the interval between scanning lines adjacent to the scanning line Is different for each position in the main scanning direction. In the optical scanning device, the optical path of the laser light differs depending on the position in the main scanning direction due to an assembly error of the optical scanning device itself or a manufacturing error of the optical component. When the optical path of the laser beam is different for each position in the main scanning direction, for example, the imaging characteristic is also different in an fθ lens or the like. For this reason, the effect of the surface tilt of the rotary polygon mirror occurs as a shift amount (hereinafter, simply referred to as the surface tilt amount) which is different for each position in the main scanning direction.

  In the prior art, no solution has been disclosed for the problem that the pitch of the scanning lines differs for each position in the main scanning direction. In order to form a uniform image without banding over the entire image area, it is necessary to make corrections for different amounts of misregistration for each position in the main scanning direction.

  The present invention has been made under such circumstances, and it is an object of the present invention to obtain good image quality by correcting image distortion and density unevenness caused by positional displacement amounts different for each position in the main scanning direction. I assume.

  In order to solve the problems described above, the present invention comprises the following configuration.

  (1) A light source having a plurality of light emitting elements, a photosensitive member which is rotated in a first direction and on which a latent image is formed by a light beam emitted from the light source, and a light beam emitted from the light source is deflected A correction method of an image forming apparatus, comprising: deflection means for moving a spot of a light beam irradiated to the photosensitive member in a second direction orthogonal to the first direction to form a scanning line, Storing the information on the positional deviation in the first direction according to the second direction of the line in the storage means, and the scanning line on the photosensitive member based on the information stored in the storage means Of the pixels of the input image based on the conversion step of converting the positions of the pixels of the input image by performing coordinate conversion such that the interval of the pixels becomes a predetermined interval, and the positions of the pixels of the input image after the coordinate conversion. Perform convolution operation on pixel values and Correction method characterized by comprising a filtering step of obtaining the pixel value of the pixel of the image.

  According to the present invention, it is possible to correct image distortion and density unevenness caused by positional displacement amounts different for each position in the main scanning direction, and to obtain excellent image quality.

FIG. 2 is a diagram showing the entire image forming apparatus of the embodiment, and FIG. Block diagram of image forming apparatus of the embodiment The figure which shows the position shift of the scanning line of an Example Block diagram illustrating the process of storing information in the memory of the embodiment The figure which shows the interpolation calculation of the main scanning direction of an Example Time chart of one scanning period in the embodiment Flow chart showing image formation processing of the embodiment Flow chart showing correction processing of the embodiment Diagram showing the misalignment of the pixels of the embodiment for each classification The figure which shows the coordinate transformation of the pixel position of the subscanning direction of an Example The figure which shows the coordinate transformation of the pixel position of the subscanning direction of an Example The figure which shows the coordinate transformation of the pixel position of the subscanning direction of an Example Diagram showing convolution function used for filter processing of the embodiment, Diagram for explaining correction values and coefficients Diagram showing filter processing for each classification of misalignment in the embodiment Flow chart showing filter processing of the embodiment Diagram showing misalignment of scanning lines in the prior art

  Hereinafter, preferred embodiments of the present invention will be exemplarily described in detail with reference to the drawings. The rotational direction of the photosensitive drum is the second direction, that is, the main scanning direction as the second direction, and the direction substantially orthogonal to the main scanning direction, that is, the first rotational direction of the photosensitive drum. In the sub-scanning direction.

<Configuration of Entire Image Forming Apparatus>
FIG. 1A is a schematic cross-sectional view of a digital full color printer (color image forming apparatus) that forms an image using toners of a plurality of colors. An image forming apparatus 100 according to an embodiment will be described with reference to FIG. The image forming apparatus 100 is provided with four image forming units (image forming units) 101Y, 101M, 101C, and 101Bk (dotted line portions) that form images by color. The image forming units 101Y, 101M, 101C, and 101Bk perform image formation using toners of yellow, magenta, cyan, and black, respectively. Y, M, C, and Bk represent yellow, magenta, cyan, and black, respectively, and the suffixes Y, M, C, and Bk will be omitted hereinafter except in the case of describing a specific color.

  The image forming unit 101 is provided with a photosensitive drum 102 which is a photosensitive member. A charging device 103, an optical scanning device 104, and a developing device 105 are provided around the photosensitive drum 102. In addition, a cleaning device 106 is disposed around the photosensitive drum 102. Below the photosensitive drum 102, an endless belt-like intermediate transfer belt 107 is disposed. The intermediate transfer belt 107 is stretched around the driving roller 108 and the driven rollers 109 and 110, and rotates in the direction of arrow B (clockwise direction) in the drawing during image formation. Further, a primary transfer device 111 is provided at a position facing the photosensitive drum 102 via the intermediate transfer belt 107 (intermediate transfer member). Further, the image forming apparatus 100 of the present embodiment includes a secondary transfer device 112 for transferring the toner image on the intermediate transfer belt 107 to the sheet S as a recording medium, and a fixing for fixing the toner image on the sheet S. A device 113 is provided.

  The image forming process from the charging process to the developing process of the image forming apparatus 100 will be described. Since the image forming process in each image forming unit 101 is the same, the image forming process will be described by taking the image forming unit 101Y as an example, and the description of the image forming process in the image forming units 101M, 101C, and 101Bk will be omitted. The charging device 103Y of the image forming unit 101Y charges the photosensitive drum 102Y rotationally driven in the direction of the arrow (counterclockwise direction) in the drawing. The charged photosensitive drum 102 </ b> Y is exposed by the laser beam shown by a dashed dotted line emitted from the light scanning device 104 </ b> Y. Thereby, an electrostatic latent image is formed on the rotating photosensitive drum 102Y (on the photosensitive member). The electrostatic latent image formed on the photosensitive drum 102Y is developed as a yellow toner image by the developing device 105Y. The same process is performed in the image forming units 101M, 101C, and 101Bk.

  The image forming process after the transfer process will be described. The primary transfer device 111 to which the transfer voltage is applied transfers the yellow, magenta, cyan, and black toner images formed on the photosensitive drum 102 of the image forming unit 101 to the intermediate transfer belt 107. Thus, the toner images of the respective colors are superimposed on the intermediate transfer belt 107. That is, toner images of four colors are transferred to the intermediate transfer belt 107 (primary transfer). The four color toner images transferred onto the intermediate transfer belt 107 are transferred by the secondary transfer device 112 onto the sheet S conveyed from the manual feed cassette 114 or the paper feed cassette 115 to the secondary transfer portion. (Secondary transfer). Then, the unfixed toner image on the sheet S is heated and fixed by the fixing device 113, and a full color image is obtained on the sheet S. The sheet S on which the image is formed is discharged to the sheet discharge unit 116.

<Photosensitive drum and light scanning device>
FIG. 1B shows the configuration of the photosensitive drum 102, the light scanning device 104, and the control unit of the light scanning device 104. The light scanning device 104 includes a multi-beam laser light source (hereinafter, laser light source) 201, a collimator lens 202, a cylindrical lens 203, and a rotary polygon mirror 204. The laser light source 201 is a multi-beam laser light source that generates laser light (light beam) by a plurality of light emitting elements. The collimator lens 202 shapes the laser light into parallel light. The cylindrical lens 203 condenses the laser beam that has passed through the collimator lens 202 in the sub-scanning direction. In the present embodiment, the laser light source 201 is described as an example of a multi-beam light source in which a plurality of beams are arranged, but the same operation is performed when a single light source is used. The laser light source 201 is driven by a multi-beam laser drive circuit (hereinafter simply referred to as a laser drive circuit) 304. The rotating polygon mirror 204 is composed of a rotating motor unit and a reflecting mirror attached to the motor shaft. Hereinafter, the surface of the reflecting mirror of the rotating polygon mirror 204 is referred to as a mirror surface. The rotary polygon mirror 204 is driven by a rotary polygon mirror drive unit 305. The optical scanning device 104 includes fθ lenses 205 and 206 on which the laser light (scanning light) deflected by the rotating polygon mirror 204 is incident. In addition, the light scanning device 104 has a memory 302 which is a storage unit in which various information is stored.

  Further, the light scanning device 104 detects a laser beam deflected by the rotary polygon mirror 204, and outputs a horizontal synchronization signal (hereinafter referred to as a BD signal) in response to the detection of the laser beam. (Hereinafter, BD 207). The laser beam emitted from the light scanning device 104 scans the photosensitive drum 102. The optical scanning device 104 and the photosensitive drum 102 are positioned such that the laser beam is scanned parallel to the rotation axis of the photosensitive drum 102. Each time the mirror surface of the rotary polygon mirror 204 scans the photosensitive drum 102 once, the light scanning device 104 scans the spot of the light beam of the multi-beam laser in the main scanning direction and scans the number of scanning lines equal to the number of laser elements. Form at the same time. In the present embodiment, the number of mirror faces of the rotary polygon mirror 204 is five, and the laser light source 201 will be described by way of example of a configuration having eight laser elements. That is, in the present embodiment, since the image formation for eight lines is performed by one scan, the rotary polygon mirror 204 scans five times per one rotation, and image formation for a total of 40 lines is performed.

  The photosensitive drum 102 is provided with a rotary encoder 301 on the rotation shaft, and detection of the rotational speed of the photosensitive drum 102 is performed using the rotary encoder 301. The rotary encoder 301 generates 1000 pulses each time the photosensitive drum 102 makes one rotation, and information on the rotational speed of the photosensitive drum 102 based on the result of measuring the time interval of the generated pulse using the built-in timer (rotation The speed data is output to the CPU 303. Note that any known speed detection technique other than the above-described rotary encoder may be used as long as the rotational speed of the photosensitive drum 102 can be detected. As a method other than the encoder, for example, there is a method of detecting the surface speed of the photosensitive drum 102 by laser Doppler or the like.

<Block diagram of CPU>
Next, the CPU 303 that controls the light scanning device 104 will be described with reference to FIG. FIG. 2 is a block diagram showing the function of the CPU 303 that executes correction processing to correct distortion and density unevenness of an image described later. The CPU 303 has a filter processing unit 501, an error diffusion processing unit 502, and a PWM signal generation unit 503. The filter processing unit 501 performs a filtering process by performing a convolution operation on the input image data. The error diffusion processing unit 502 performs error diffusion processing on the image data after filter processing. The PWM signal generation unit 503 performs PWM conversion on the image data after error diffusion processing, and outputs a PWM signal to the laser drive circuit 304 of the optical scanning device 104.

  The CPU 303 further includes a filter coefficient setting unit 504, a filter function output unit 505, and a correction value setting unit 506. The filter function output unit 505 outputs data (for example, data of a table) of a function used for the convolution operation to the filter coefficient setting unit 504, and for the function used for the convolution operation, for example, linear interpolation or bicubic interpolation There is. The correction value setting unit 506 calculates the amount of positional deviation of the scanning line based on the information of the amount of positional deviation read from the memory 302 of the light scanning device 104 and the surface synchronization signal input from the surface specifying unit 507. The correction value setting unit 506 calculates a correction value based on the positional deviation amount of the scanning line, and outputs the calculated correction value to the filter coefficient setting unit 504. The filter coefficient setting unit 504 is used for the filter processing by the filter processing unit 501 based on the information of the convolution function input from the filter function output unit 505 and the correction value of the scanning line input from the correction value setting unit 506. Filter coefficients to be calculated. The filter coefficient setting unit 504 sets the calculated filter coefficient in the filter processing unit 501.

  The CPU 303 further includes a surface identification unit 507. The surface specifying unit 507 is a mirror surface of the rotating polygon mirror 204 based on the HP signal input from the home position sensor (hereinafter referred to as HP sensor) 307 of the light scanning device 104 and the BD signal input from the BD 207. Identify The surface identification unit 507 outputs the identified information on the mirror surface to the correction value setting unit 506 as a surface synchronization signal.

  As shown in FIG. 1B, image data is input to the CPU 303 from an image controller (not shown) that generates image data. Further, the CPU 303 is connected to the rotary encoder 301, the BD 207, the memory 302, the laser drive circuit 304, and the rotary polygon mirror drive unit (hereinafter, mirror drive unit) 305. The CPU 303 detects the writing position of the scanning line based on the BD signal input from the BD 207, and detects the rotational speed of the rotating polygon mirror 204 by counting the time interval of the BD signal. Further, the CPU 303 outputs an acceleration / deceleration signal for instructing the mirror drive unit 305 to accelerate / decelerate so that the rotary polygon mirror 204 has a predetermined speed. The mirror drive unit 305 supplies a drive current to the motor unit of the rotating polygon mirror 204 according to the acceleration / deceleration signal input from the CPU 303 to drive the motor 306.

  As shown in FIG. 2, an HP sensor 307 is mounted on the rotary polygon mirror 204, and the HP sensor 307 sends an HP signal to the CPU 303 at a timing when the rotary polygon mirror 204 turns to a predetermined angle. Output. The surface specifying unit 507 of the CPU 303 detects which of the five mirror surfaces of the rotary polygon mirror 204 scans the laser light at the timing when the HP signal from the HP sensor 307 is detected, that is, the mirror being scanned Identify the face. Once the mirror surface is specified, the surface specifying unit 507 continues to specify the mirror surface based on the BD signal output from the BD 207 thereafter. Each time the arbitrary mirror surface of the rotating polygon mirror 204 scans the laser light once, the BD 207 outputs one BD signal pulse, so that the CPU 303 counts the BD signal to specify the mirror surface of the rotating polygon mirror 204. It is possible to continue.

  The memory 302 stores position information of each mirror surface of the rotary polygon mirror 204 and position information of the multi-beam laser, and the CPU 303 reads each information. The CPU 303 calculates the position of each scanning line based on the information read from the memory 302, and adds information for correcting the position of each scanning line from the calculated position of each scanning line and the input image data. Calculated image data. The CPU 303 outputs the light emission amount data to the laser drive circuit 304 based on the image data to which the information in which the position of each scanning line is corrected is added. In the present embodiment, the laser drive circuit 304 performs light amount control by controlling the lighting time for each pixel by PWM (pulse width modulation) control based on the light emission amount data input from the CPU 303. In addition, when performing light amount control, it is not necessary to necessarily use PWM control, and light amount control may be performed by AM (amplitude modulation) control which controls a peak light amount for each pixel.

<Scan position information>
Next, scanning position information stored in the memory 302 will be described using FIG. 3 and Table 1. FIG. 3 shows the positional deviation of each scanning line from the ideal position. The scanning line which each laser of the multi beam laser which has eight light emission points scans is set to LD1, LD2, LD3, LD4, LD5, LD6, LD7, LD8. Here, the ideal spacing of each scan line is determined by the resolution. For example, in the case of an image forming apparatus with a resolution of 1200 dpi, the ideal interval of each scanning line is 21.16 μm. Assuming that LD1 is a reference position, ideal distances D2 to D8 of scan lines LD2 to LD8 from scan line LD1 are calculated by equation (1).
Dn = (n-1) × 21.16 μm (n = 2 to 8) (1)
For example, the ideal distance D4 from the scan line LD1 to the scan line LD4 is 63.48 μm (= (4-1) × 21.16 μm).

  Here, the scanning line spacing has an error due to an error in the element spacing of the multi-beam laser and a variation in magnification of the lens. The positional deviation amounts of the scanning lines LD2 to LD8 with respect to the ideal position determined by the ideal distances D2 to D8 are X1 to X7. For the A-face of the rotary polygon mirror 204, for example, the positional deviation amount X1 of the scanning line LD2 is between the ideal position of the scanning line LD2 (hereinafter, the same applies to line 2 and other scanning lines) and the actual scanning line. It will be a difference. Also, for example, the positional deviation amount X3 of the scanning line LD4 is a difference between the line 4 and the actual scanning line.

  Due to manufacturing variations of the mirror surfaces of the rotary polygon mirror 204, the rotary polygon mirror 204 does not have completely parallel angles of the mirror surfaces with respect to the rotation axis, but has angular variations from mirror surface to mirror surface. Further, in the scanning of the laser light on each mirror surface, the amount of deviation differs depending on the position in the main scanning direction. In this embodiment, the image area in the main scanning direction is divided into a predetermined number of blocks, for example, five blocks, and the amount of positional deviation corresponding to each of the five blocks is stored in the memory 302 for each mirror surface. As described above, storing the position information in the block unit in the memory 302 makes it possible to reduce the capacity as compared with the case where the position information is held for each pixel.

The amount of positional deviation of each of the mirror faces of the rotary polygon mirror 204 with respect to the ideal position is represented by Y1A to Y5E when the number of mirror faces of the rotary polygon mirror 204 is five and the number of blocks in the main scanning direction is five. Here, A to E represent five planes of the rotary polygon mirror 204, and 1 to 5 represent five blocks in the main scanning direction. For example, the amounts of deviation from the ideal position of the first to fifth blocks of the scan line (line 1) of the LD1 on the A-side of the rotary polygon mirror 204 are represented as Y1A, Y2A, Y3A, Y4A, Y5A. Similarly, the amounts of deviation from the ideal position of the first to fifth blocks of the scan line (line 9) of the LD 1 on the B side of the rotary polygon mirror 204 are represented as Y1B, Y2B, Y3B, Y4B, and Y5B. The displacement amount of the b-th block in the main scanning direction of the n-th laser beam of the multi-beam and the mirror surface of the m-th surface of the rotary polygon mirror 204 is assumed to be Znbm. Then, the positional deviation amount Znbm is expressed by Expression (2) using the positional deviation amounts X1 to X7 in the sub scanning direction of each scanning line and the positional deviation amounts YA to YE of the mirror surfaces.
Znbm = Ybm + X (n-1) (n = 1 to 8, b = 1 to 5, m = A to E) Formula (2)
(However, X (0) = 0)
For example, the positional deviation amount Z43A for the third block of the scanning line LD4 on the A side of the rotary polygon mirror 204 can be obtained from the equation (2) as Z43A = Y3A + X3. Further, the positional deviation amount Z15B for the fifth block of the scan line LD1 on the B-side of the rotary polygon mirror 204 can be obtained from the equation (2) as Z15B = Y5B.

  When calculating the displacement amount Znbm by the operation of equation (2), the data used to calculate the displacement amount Znbm is the number of mirror surfaces of the rotating polygon mirror 204, the number of elements of the multi-beam laser, and the blocks in the main scanning direction It suffices to have the number of data corresponding to the number. Here, Table 1 shows an address map of misalignment data stored in the memory 302.

  As shown in Table 1, information of displacement amounts (described as position information) X1 to X7 from the scan line LD2 to the scan line LD8 is stored at addresses 1 to 7 of the memory 302. Further, information of displacement amounts Y1A to Y5A from block 1 to block 5 of the A-th surface of the mirror surface of the rotary polygon mirror 204 is stored at addresses 8 to 12 of the memory 302. Also, information of displacement amounts Y1B to Y5B from block 1 to block 5 on the B surface of the mirror surface of the rotary polygon mirror 204 is stored at addresses 13 to 17 of the memory 302. Further, information of displacement amounts Y1C to Y5C from the block 1 to the block 5 of the C surface of the mirror surface of the rotary polygon mirror 204 is stored at the address 18 to the address 22 of the memory 302. Also, information of displacement amounts Y1D to Y5D from block 1 to block 5 on the D-th surface of the mirror surface of the rotary polygon mirror 204 is stored in the address 23 to the address 27 of the memory 302. Further, information of displacement amounts Y1E to Y5E from block 1 to block 5 of the E surface of the mirror surface of the rotary polygon mirror 204 is stored in the address 28 to the address 32 of the memory 302.

(Memory storage operation)
The information on the amount of positional deviation stored in the memory 302 stores, for example, data measured in the adjustment process of the optical scanning device 104 in a factory or the like. The image forming apparatus may be provided with means for detecting the position of the scanning line scanned by the laser light emitted from the laser light source 201, and the information stored in the memory 302 may be updated in real time. A well-known technique may be used as a position detection means of the subscanning direction of scanning light. For example, the position detection may be performed by a CMOS sensor or a PSD (Position Sensitive Detector) disposed inside the optical scanning device or near the photosensitive drum. Alternatively, a triangular slit may be disposed on the surface of a PD (photo diode) disposed inside the light scanning device or in the vicinity of the photosensitive drum, and position detection may be performed from the output pulse width of the PD.

  FIG. 4 shows, as an example, a block diagram when information is stored in the memory 302 of the optical scanning device 104 at a factory or the like. The same components as those in FIG. 2 are assigned the same reference numerals and descriptions thereof will be omitted. In the adjustment process of the optical scanning device 104, the measurement tool 400 is disposed at a position corresponding to the position of the photosensitive drum when the optical scanning device 104 is mounted on the image forming apparatus. The measurement tool 400 includes a measurement unit 410 and a calculation unit 402. The calculation unit 402 is configured to receive a surface synchronization signal from the surface identification unit 507 of the CPU 303 in FIG. In the CPU 303 of FIG. 4, only the surface identification unit 507 is drawn. First, the light scanning device 104 causes the measuring unit 410 to emit a laser beam. The measuring unit 410 has a triangular slit 411 and a PD 412, and the light beam scanned from the light scanning device 104 indicated by a dashed dotted arrow in the figure scans the triangular slit 411. The measuring unit 410 measures the position in the sub-scanning direction of the scanning line based on the information of the light beam input to the PD 412 via the triangular slit 411. The measuring unit 410 outputs information on the measured position of the scanning line for each mirror surface of the rotary polygon mirror 204 in the sub-scanning direction depending on the main scanning direction (hereinafter referred to as plane-by-plane data) to the computing unit 402.

  On the other hand, the HP signal from the HP sensor 307 of the light scanning device 104 is input to the surface identification unit 507, and the BD signal is input from the BD 207. Thereby, the surface specifying unit 507 specifies the mirror surface of the rotary polygon mirror 204, and outputs the information of the specified mirror surface to the computing unit 402 as a surface synchronization signal. Arithmetic unit 402 sets the main scanning direction of the scanning line measured by measuring unit 410 to the address on memory 302 of optical scanning device 104 according to the information on the mirror surface of rotary polygon mirror 204 input from surface identification unit 507. Write the information of the position in the sub scanning direction depending on. As described above, the information (X1 to X7) of the positional deviation amount of the scanning line generated due to the variation of the eight elements of the laser light source 201 is stored in the memory 302. Further, information (Y 1 A to Y 5 E) of positional deviation amount for each block of the scanning line which is generated due to the surface inclination of the mirror surface of the rotary polygon mirror 204 is also stored in the memory 302.

(Description of interpolation calculation processing in the main scanning direction)
In this embodiment, as described in Table 1, the image area in the main scanning direction is divided into five blocks, and the amount of positional deviation corresponding to each block is held in the memory 302 for each surface. Therefore, when the scanning of the laser light of the predetermined block is completed and the scanning of the laser light of the next block is started, a step is generated in the positional deviation amount. For example, as shown in FIG. 5, in order to reduce the level difference of the positional displacement amount between blocks, interpolation processing using linear interpolation is performed on the positional displacement amount of each block, and the position in the main scanning direction It may be used as a deviation amount.

  FIG. 5 is a graph showing the position in the main scanning direction on the horizontal axis, and the amount of positional deviation (μm) in the sub-scanning direction on the vertical axis. In FIG. 5, the positional deviation amount for each block is described for the first block to the fifth block of the image area of one scanning line in the main scanning direction. For example, in the third block (b = 3), the displacement amount is 3 μm. The positional deviation amount for each block changes stepwise as shown by a solid line in FIG. In this embodiment, as shown by a broken line (after interpolation (for example, linear interpolation)) by performing interpolation processing, for example, linear interpolation before the positional displacement amount for each block (before interpolation processing (data in memory)), block The step of the positional displacement amount when switching is eliminated. For this reason, the effect of preventing the image shift when switching the block can be obtained.

<How to calculate misalignment amount>
FIG. 6 shows control timing within one scanning period of the n-th laser beam in the sub scanning direction of the present embodiment. (1) shows the CLK signal corresponding to the pixel cycle per pixel, and (2) shows the input timing of the BD signal from the BD 207 to the CPU 303. (3) and (5) indicate input timings of the image data DATAN (N = 1, 2,...) Before the filter operation to the CPU 303. (4) indicates the timing at which the positional deviation amount CnN (N = 1, 2,...) Corresponding to each pixel is calculated. (6) indicates the timing at which the image data DATAN ′ (N = 1, 2,...) Subjected to the filter operation processing is output to the laser drive circuit 304. Note that N at the end of DATAN and DATAN 'represents the number of a pixel in one scanning line in the main scanning direction.

  When the BD signal output from the BD 207 is used as a reference, the time from the timing when the BD signal is output to the timing when the laser light reaches the front end of the image area in the main scanning direction of the photosensitive drum 102 is T1. Further, the time from the timing when the BD signal is output to the timing when the laser light reaches the end of the image area in the main scanning direction of the photosensitive drum 102 is T2. The image forming apparatus, after detecting the BD signal by the CPU 303, stands by until a predetermined time T1 elapses, then starts image formation, and after detecting the BD signal, after a predetermined time T2 elapses, one scanning line Finish the image formation. The CPU 303 calculates, for each scan, the amount of positional deviation of the scanning line in the image area until the predetermined time T2 elapses after the predetermined time T1 elapses, that is, after the filter processing by the filter processing unit 501. Image data is sent to the laser drive circuit 304 to form an image. Here, the amount of positional deviation with respect to the pixel of interest is calculated in the time of one cycle of the CLK signal of (1). In addition, the filter processing unit 501 performs the filtering process on the pixel of interest in the time of one cycle of the CLK signal of (1). Then, one clock cycle after the image data before the filter operation is input, the image data after the filter operation is output to the laser drive circuit 304 (broken line frame in FIG. 6). ΔT is a time interval of the BD signal output from the BD 207, which is a time per scan.

  In the present embodiment, the positional shift amount (CnN) of each pixel shown in (4) of FIG. 6 is calculated using the positional shift amounts of five blocks (b = 1 to 5) divided in the main scanning direction. Ru. As the positional displacement amount of each pixel, as described in FIG. 5, a value obtained by linearly interpolating the positional displacement amount of each block and distributing the positional displacement amount of each pixel may be used. Thus, one positional deviation amount may correspond to one pixel in the main scanning direction, or one positional deviation amount may correspond to a plurality of pixels. By the above operation, the CPU 303 performs calculation of displacement amount, filter processing, and transmission of image data to the laser drive circuit 304 between time T1 and time T2 to form an image for one scan.

(Calculation of displacement amount of Nth pixel)
FIG. 7 is a flowchart showing a process performed by the CPU 303 to form an image while calculating the amount of positional deviation of the Nth pixel in the main scanning direction (also referred to as the Nth pixel). The CPU 303 calculates an amount of positional deviation for each scanning line at the time of image formation, and performs image formation. In step (hereinafter referred to as S) 7001, the CPU 303 sets the position n in the sub-scanning direction to one. In step S7002, the CPU 303 determines whether a BD signal has been input from the BD 207. If the CPU 303 determines in S7002 that the BD signal is input, the CPU 303 stops a timer (not shown) measuring a time interval which is a cycle of the BD signal, reads a timer value, and stores the timer value in an internal register. Then, in order to measure the time interval until the next BD signal is received, the CPU 303 resets and starts a timer (not shown), and proceeds to the process of S7003. When the CPU 303 has two or more timers (not shown), different timers may be alternately used each time a BD signal is received to perform time measurement. Further, although the time interval of the measured BD signal is stored in the internal register of the CPU 303 here, it may be stored, for example, in a RAM memory (not shown) of the CPU 303. If the CPU 303 determines in S7002 that the BD signal is not input, the processing of S7002 is repeated to wait for the BD signal to be input.

  In step S7003, the CPU 303 determines whether the time T1 has elapsed after detecting the BD signal by referring to the timer. If the CPU 303 determines in step S7003 that the time T1 has elapsed, it determines that it has entered an image area in the main scanning direction, and proceeds to the processing of step S7004. If the CPU 303 determines in step S7003 that the time T1 has not elapsed, it determines that it is still a non-image area in the main scanning direction, and repeats the processing of step S7003. In step S7004, the CPU 303 sets the variable N = 1. Here, the variable N is a variable corresponding to the pixel number from the pixel at the top of the image writing in the main scanning direction. In S7005, the CPU 303 calculates the displacement amount (CnN) of the Nth pixel in the main scanning direction (FIG. 6 (4)), and performs filter processing on the image data based on the displacement amount (FIG. ), (6)). In step S7006, the CPU 303 determines whether N = 14000. If it determines that N = 14000, the process proceeds to step S7008. If the CPU 303 determines in S7006 that N is not 14000, it proceeds to the process of S7007. In S7007, the CPU 303 adds 1 to N (N = N + 1), and returns to the process of S7005 in order to perform an operation on the next pixel in the main scanning direction. Here, for example, when an image is formed on a recording sheet of A4 size (the length in the main scanning direction is 297 mm) at a resolution of 1200 dpi, the number of pixels is about 14000. For this reason, in the main scanning direction, the pixel number N is changed to N = 1 to 14000 to calculate the amount of positional deviation of each pixel, thereby calculating the amount of positional deviation for one scan. When the resolution is changed, the threshold in S7006 also becomes a value corresponding to the resolution.

  In step S7008, the CPU 303 adds 1 to the position n in the sub scanning direction (n = n + 1), and the processing proceeds to step S7009. In step S7009, the CPU 303 determines whether processing for one page has ended based on the position n in the sub scanning direction. If it determines that the processing has ended, the processing ends, and if it is determined that the processing has not ended. , And returns to the process of S7002.

(Calculation of misregistration amount)
The formula for calculating the positional deviation amount CnN calculated by the CPU 303 in S7005 will be described in detail. The positional deviation amount CnN with respect to the pixel number N in the main scanning direction of the nth scanning line is determined as follows. That is, the sum of positional deviations is calculated by adding the positional deviation A due to the fluctuation of the rotational speed of the photosensitive drum 102 or the rotary polygon mirror 204 and the positional deviation B depending on the main scanning direction for each scanning line. Desired. Assuming that the rotational speed of the photosensitive drum 102 is Vd, the rotational speed of the rotary polygon mirror 204 is Vp, and one scanning time is ΔT (see FIG. 6), the rotational speed Vd of the photosensitive drum 102 and the rotational speed Vp of the rotary polygon mirror 204 The positional deviation amount A resulting from the difference is calculated from the following equation (3).
A = (Vd−Vp) × ΔT formula (3)

Here, ΔT is a time corresponding to the interval of the output timing of the BD signal, and the positional deviation amount A is a difference of the rotational speed Vd of the photosensitive drum 102 and the rotational speed Vp of the rotary polygon mirror 204 for one scanning period. The positional shift amount of the scanning line which moves between is shown. Here, as described above, the rotation speed Vp of the rotary polygon mirror 204 is obtained based on the printing speed Vpr. The printing speed Vpr is determined by the equations (4) and (5) from the relationship between one scanning time ΔT and the number of multi-beams (eight beams in this embodiment).
Vp = number of beams × 21.16 ÷ ΔT equation (4)
ΔT = 1 ÷ (number of mirror faces of rotary polygon mirror 204 × number of rotations per second of rotary polygon mirror 204) (5)

On the other hand, as the positional deviation amount B, a value calculated from the above-mentioned equation (2) is used.
B = Znbm (6)
The CPU 303 adds the positional displacement amount A calculated from the equation (3) and the positional displacement amount B calculated from the equation (6) to calculate the sum (total value = A + B) of the positional displacement amounts. The CPU 303 holds the total amount of positional deviation calculated in step S7005 in the internal register of the CPU 303. Here, the amount of positional deviation (= A + B) held in the register is read out at the time of filter processing to be described later and used for calculation.

  In the present embodiment, the filter operation is performed based on the image data of a plurality of scanning lines and the amount of positional deviation. For example, when the range of the filter calculation is L = 3, the image data of the upper and lower three pixels from the target line is referred to, the positional deviation amount of each scanning line in the range between the target line and the upper and lower three pixels is calculated, Assumed to be performed.

  Here, the amount of positional deviation of the scanning line corresponding to the target line is calculated in the period immediately before the image formation. Further, for the scan line scanned before the target line, the calculation result of the positional deviation amount calculated for the scan line scanned earlier is used. For a scan line scanned at a timing later than the line of interest, the positional deviation amount B is determined based on the information on the mirror surface of the rotary polygon mirror 204 corresponding to the scan line to be scanned later and the multibeam position information. . The rotational speed Vp of the rotary polygon mirror 204 and the rotational speed Vd of the photosensitive drum 102 are determined as follows. That is, based on the value detected at the timing when the laser beam was scanned before and the value detected at the timing when the target line (current scan line) scanned, the rotational speed Vp in the scan line to be scanned next Assume that Vd is predicted and obtained.

(Correction of the position of pixels of the input image in the sub scanning direction)
In the present embodiment, the CPU 303 corrects the image data based on the positional deviation amount in the sub-scanning direction of the scanning line by the laser light, and outputs the corrected image data to the laser drive circuit 304. Hereinafter, the flowchart of FIG. 8 will be described. FIG. 8 is a flow chart for explaining correction processing for correcting density unevenness and banding that occur due to positional deviation in the sub scanning direction. In step S3602, the CPU 303 reads the positional deviation amount in the sub scanning direction stored in the memory 302. Specifically, the CPU 303 reads from the memory 302 the position information X1 to X7 of the LD2 to LD8 described in Table 1 and the position information Y1A to Y5E corresponding to the blocks of the A to E planes of the rotary polygon mirror 204. In this embodiment, after correcting the pixel position in the sub scanning direction of the input image data based on the positional deviation amount in the sub scanning direction, filter processing is performed to output pixel data, that is, the density. Do.

(Displacement of scanning line)
The positional deviation of the scanning line can be roughly classified into four. First, in the positional deviation state, (a) when the position of the scanning line on the photosensitive drum 102 (hereinafter, the scanning position) is shifted in the advancing direction with respect to the ideal scanning position, (b) on the photosensitive drum 102 The scan position may shift in the return direction with respect to the ideal scan position. In the positional deviation state, (c) when the scanning position interval on the photosensitive drum 102 is close to the ideal scanning position interval, the (d) scanning position on the photosensitive drum 102 is reversed. The spacing may be sparse relative to the spacing of the ideal scan position. A specific example of these positional deviations in the sub-scanning direction is shown in FIG. In the figure, the broken line indicates the scanning position, and (1) to (5) in the figure indicate the order of scanning. In this embodiment, eight beams are simultaneously scanned, but in the following description, it is assumed that the order is changed for each beam sequentially arranged in the sub-scanning direction. The left column in FIG. 9 indicates the ideal scanning position, and the right column indicates the scanning position on the photosensitive drum 102. For the scan numbers (1) to (5), S1 to S5 indicate the amount of displacement from the ideal scan position. The unit of positional deviation is expressed based on the ideal beam interval (21.16 μm at 1200 dpi) as 1, and the forward direction (hereinafter simply referred to as the forward direction) of the light beam in the sub scanning direction is a positive value. There is. Further, the return direction of the light beam in the sub scanning direction (hereinafter simply referred to as the return direction) is a negative value. Furthermore, in order to explain the appearance of the image, one pixel aligned in the sub-scanning direction is indicated by a circle on the scanning line. The color of the circle represents the density.

  FIG. 9A shows an example in which the scanning position on the photosensitive drum 102 is uniformly shifted by 0.2 in the advancing direction from the ideal scanning position. Hereinafter, the displacement amount as shown in FIG. 9A is referred to as a shift amount of +0.2. FIG. 9B shows an example where the scanning position on the photosensitive drum 102 is uniformly shifted by 0.2 in the return direction from the ideal scanning position. Hereinafter, the positional deviation amount as shown in FIG. 9B is referred to as a shift amount of −0.2 line. In FIG. 9A and FIG. 9B, since the scanning positions are uniformly shifted, the intervals of the scanning positions on the photosensitive drum 102 are all one.

  In FIG. 9C, at the predetermined scanning position on the photosensitive drum 102, the positional deviation amount is zero. However, as the scan position moves forward from the scan position with a shift amount of 0, the shift amount in the forward direction increases, and as the scan position moves back from the scan position with a shift amount of 0, the shift amount in the return direction decreases. growing. For example, S3 = + 0 for scan number (3), S2 = + 0.2 for scan number (2), S1 = + 0.4 for scan number (1), and S4 = −0 for scan number (4) In the scan number (5), S5 = -0.4. In FIG. 9C, the distance between scanning positions is 0.8, which is smaller than one. Hereinafter, the state of misalignment as shown in FIG. 9C is referred to as dense at intervals of (1-0.2) lines.

  In FIG. 9D, at a predetermined scanning position on the photosensitive drum 102, the positional deviation amount is zero. However, the amount of displacement in the return direction increases as the scan position moves forward from the scan position with a displacement amount of 0, and the amount of displacement in the advance direction increases as the scan position moves back from the scan position with a displacement amount of 0 growing. For example, S3 = + 0 for scan number (3), S2 = -0.2 for scan number (2), S1 = -0.4 for scan number (1), and S4 = for scan number (4) In the scan number (5), S5 = + 0.4. In FIG. 9D, the interval between the scanning positions is 1.2, which is larger than one. Hereinafter, the state of positional deviation as shown in FIG. 9D is referred to as sparse at intervals of (1 + 0.2) lines.

  In the dense state as shown in FIG. 9C, not only positional deviation occurs, but the scanning positions are closely spaced, so that the pixels are densely packed on the photosensitive drum 102, and the pixel value per predetermined area is The concentration is increased by the increase. On the contrary, in the sparse state as shown in FIG. 9D, not only positional deviation occurs but also the spacing between scanning positions becomes sparse, so that the pixels become sparse on the photosensitive drum 102, and a predetermined area per area is obtained. The pixel value of is reduced and the density is reduced. In the electrophotographic process, the density difference may be further emphasized due to the relationship between the depth of the latent image potential and the development characteristics. Further, if density density as shown in FIG. 9C and density density as shown in FIG. 9D alternately occurs, periodic shading becomes moiré, and depending on spatial frequency, it becomes easy to visually detect even the same amount.

  It returns to description of the flowchart of FIG. In step S3603, the CPU 303 causes the correction value setting unit 506 to generate correction attribute information for each pixel of the input image. In this embodiment, the pixel position in the sub-scanning direction of the input image is subjected to coordinate conversion in advance, and then interpolation is performed to simultaneously perform local density correction while preserving the density of the input image as well as correcting positional deviation. Make it possible. Here, the correction attribute information specifically refers to a correction value CnN to be described later. Here, n indicates the number of the scanning line (or pixel) in the sub-scanning direction, and N indicates the number of the pixel in the main scanning direction. The correction value CnN means the correction value of the Nth pixel in the main scanning direction on the nth scanning line in the subscanning direction. In the following description, the N-th pixel in the main scanning direction of each scanning line is described, and the correction value CnN is simply C or Cn.

(Coordinate transformation)
The coordinate conversion method of the present embodiment will be described with reference to FIGS. In the graphs of FIGS. 10 to 12, the horizontal axis represents the pixel number n, and the vertical axis represents the pixel position (also the scanning position) y in the sub scanning direction (y 'after coordinate conversion), and the unit is a line. 10 and 12 correspond to FIGS. 9A to 9D, respectively. The graphs on the left side of FIGS. 10 and 12 show the state before coordinate conversion, and the graphs on the right side show the state after y axis coordinate conversion. Square dots plotted on the graph represent scanning positions on the photosensitive drum 102, and circular dots represent ideal scanning positions.

(When shifting in the direction of advance and return)
The graph on the left in FIG. 10A will be described in order. In the graph before the coordinate conversion, the ideal scanning position plotted with circles is, for example, the pixel position y in the sub-scanning direction is 2 with respect to the pixel number 2, the pixel number n and y coordinate are equal, and the inclination is It is a straight line of 1 (indicated by an alternate long and short dash line). The straight line of a dashed dotted line is expressed by the following equation (7).
y = n ... Formula (7)

With respect to the ideal scan position plotted by a circle, the scan position plotted by a square is shifted by the S (= 0.2) line in the lead direction (y-axis + direction) as described in FIG. 9A. doing. Therefore, the scanning position plotted by a square is a straight line (indicated by a solid line) expressed by the following equation (8) offset with the slope being 1.
y = n + S (8)

In this embodiment, coordinate conversion is performed so that the actual scanning position is converted to the ideal scanning position. Therefore, in the case of the example shown in FIG. 10A, coordinate conversion may be performed using the following equation. In addition, C of Formula (9) becomes a correction amount.
y '= y + C (9)
Therefore, the correction amount C is expressed by the shift amount S and the following equation (10).
C = -S .. Formula (10)

By the equation (9) for coordinate conversion and the equation (10) for obtaining the correction amount C, the equations (7) and (8) are transformed as shown by the following equations (11) and (12), respectively.
y ′ = y + C = n + (− S) = n−S formula (11)
y ′ = y + C = (n + S) + C = (n + S) + (− S) = n formula (12)
In FIG. 10B, when the shift amount is S = −0.2, the equations (7) to (12) are similarly established, and can be described similarly to FIG. 10 (a). As shown in FIGS. 10 (a) and 10 (b), in the case of a scanning line in which scanning lines are not sparse or shifted and are shifted in the advancing or returning direction, straight lines before and after conversion. Has a constant slope.

(If sparseness occurs)
Here, coordinate transformation which can be applied to the case of FIG. 12 where scan positions are sparse and sparse, shift and sparse, and combinations of FIGS. 10 and 12 will be described. 11A shows the relationship between the pixel number and the scanning position, the horizontal axis is the pixel number n, the vertical axis y is the scanning position in the sub scanning direction, and the square dot is a plot of the scanning position on the photosensitive drum 102. is there. In FIG. 11A, the scanning line on the photosensitive drum 102 is dense in the range of pixel number n ≦ 2, and the scanning line on the photosensitive drum 102 is sparse in the range of pixel number n ≧ 2.

As shown in FIG. 11A, when the pixel number n 2 2 is dense, and the pixel number n 2 2 is sparse, the slope of the straight line at the pixel number n 2 2 and the pixel number n 2 2 The slope of the straight line is different, and it has a curved shape at pixel number n = 2. In FIG. 11A, a function representing a change in scanning position passing through a square dot is represented by ft (n) and is represented by a solid line. The function ft (n) representing the scanning position is expressed by the following equation (13).
y = ft (n)-Formula (13)
Next, the function ft '(n) representing the scanning position after the coordinate conversion is expressed by the following equation, when the function after the coordinate conversion of the y axis which is the scanning position in the sub scanning direction is represented by ft' (n). It is expressed by equation (14).
y '= ft' (n) ... Formula (14)

In this embodiment, coordinate conversion is performed by expanding or contracting the y-axis or shifting so that the scanning positions after coordinate conversion become uniform. For this reason, the function ft ′ (n) representing the scanning position after coordinate conversion satisfies the condition represented by the following equation (15).
ft '(n) = n .. Formula (15)
Expression (15) means that, for example, for the pixel number 2, the pixel position y ′ (= ft ′ (2)) in the sub-scanning direction after coordinate conversion is 2.

The broken line connecting FIG. 11 (a) and FIG. 11 (b) shows, from left to right, the correspondence from the original coordinate position of the y axis to the coordinate position of the y 'axis after coordinate conversion. The lower half (corresponding to n ≦ 2) of the axis is stretched, and the upper half (corresponding to n ≧ 2) is contracted. A procedure for obtaining coordinates after coordinate conversion of each pixel of input image data by coordinate conversion in FIGS. 11 (a) to 11 (b) will be described with reference to FIGS. 11 (c) and 11 (d). 11 (c) and 11 (d), as in FIGS. 11 (a) and 11 (b), the horizontal axis is the pixel number n, and the vertical axis y (or y ') is the scanning position in the sub-scanning direction FIG. 11C shows the state before coordinate conversion, and FIG. 11D shows the state after coordinate conversion. The relationship between the pixel number n of the input image data and the coordinate position y is shown below. First, a broken line shown in FIG. 11C is a function fs (n) representing an ideal scanning position before coordinate conversion, and is expressed by the following equation (16).
y = fs (n) (16)
Further, in the present embodiment, since the pixel spacing in the sub-scanning direction of the input image data is uniform, the function fs (n) is expressed by the following equation.
fs (n) = n (17)
The scanning position of the y ′ coordinate after the coordinate conversion to the target pixel number ns of the input image data is obtained in the following three steps. First, in the first step, when the y coordinate of the ideal scanning position corresponding to the pixel number ns of the input image data is ys, ys can be obtained by the following equation (18).
ys = fs (ns) formula (18)
A pixel number nt having the same scanning position before coordinate conversion on the photosensitive drum 102 (solid line) is determined ((1) in FIG. 11C). Here, the scanning position on the photosensitive drum 102 is represented by a function y = ft (n), and the relationship ys = ft (nt) is established. Assuming that the inverse function of the function ft (n) is ft ⁻¹ (y), the pixel number nt is expressed by the following equation (19).
nt = ft ⁻¹ (ys) formula (19)

In the second step, the y 'coordinate (referred to as yt) after coordinate conversion corresponding to the pixel number nt of the scanning position on the photosensitive drum 102 is converted to the following equation using the function ft' (n) after coordinate conversion It calculates | requires by (20) ((2) of FIG.11 (d)).
yt = ft '(nt) ... Formula (20)
Since the pixel number ns can be arbitrarily selected, an equation for obtaining the position yt of the y 'coordinate after coordinate conversion from the pixel number ns is a function for obtaining the y' coordinate in calculation from the pixel number n of the input image data It corresponds to fs' (n). Therefore, the general formula represented by Formula (17) is derived | led-out as follows from Formula (18)-Formula (20). A function indicating an ideal scanning position indicated by a broken line after coordinate conversion is represented by y ′ = fs ′ (n) ((3) in FIG. 11D).
yt = fs' (ns) = ft '(nt) = ft' (ft- ¹ (ys))
= Ft '(ft ^-1 (fs (ns)))
Generalize ns to n,
fs '(n) = ft' (ft- ¹ (fs (n))) .. Formula (21)

Further, the equation (17) and the equation (15) are substituted into the equation (21) with the distance 1 between the pixel interval of the input image data and the interval of the scanning position after coordinate conversion being equal. Then, Expression (21) is expressed as Expression (22) using the inverse function ft ⁻¹ (n) of the function ft (n) that derives the scanning position from the pixel number n.
fs' (n) = ft- ¹ (n) (22)

Formula (8) which the scanning position shown to FIG. 10 (a) and FIG. 10 (b) shifted uniformly in the advancing direction and the return direction, Formula (11) which calculates | requires the position after coordinate conversion of the input image data Is also in the inverse function relationship, and the formation of equation (22) can be confirmed. Further, when the density y is generated at the scanning positions as shown in FIGS. 12A and 12B, the function y representing the scanning position before coordinate conversion has a slope passing (n0, y0). In the case of a straight line of k, it can be expressed by the following equation (23).
fs (n) = y = k x (n-n0) + y0 formula (23)
In order to obtain the pixel position after coordinate conversion of the y-axis of the input image data, the inverse function ((1 / k) × (y−y0) + n0) is obtained from the equations (21) and (22) Since it is sufficient to substitute the pixel number n for the inverse function, the following equation (24) is derived.
y ′ = (1 / k) × (n−y0) + n0 formula (24)
In the case where the distance between the scanning lines shown in FIG. 12 (a) is small and the distance between the scanning lines shown in FIG. 12 (b) is small, the position of the scanning line on the photosensitive drum 102 after coordinate conversion is It can be represented by (24). Further, the correction value Cn of the pixel number n in the sub scanning direction can be obtained from Cn = fs ′ (n) −fs (n).

Specifically, in FIG. 12A, n0 = y0 = 3 and k = 0.8.
fs' (n) = (1 / 0.8) x (n-3) + 3 ... Formula (25)
It becomes. For example, in pixel number 3, fs' (3) = 3.00, and the correction value C3 is 0.00 (= 3.00-3.00). In pixel number 5, fs' (5) = 5.50, and the correction value C5 is +0.50 (= + 5.50-5.00). The values of the correction values C1 to C5 when the scanning position is dense are shown in FIG.

Further, in FIG. 12 (b), n0 = y0 = 3 and k = 1.2,
fs' (n) = (1 / 1.2) x (n-3) + 3 ... Formula (26)
It becomes. For example, in pixel number 3, fs' (3) = 3.000, and the correction value C3 is 0.000 (= 3.000-3.000). In pixel number 5, fs' (5) = 4.667, and the correction value C5 is -0.333 (= 4.667-5.000). The values of the correction values C1 to C5 when the scanning position is sparse are shown in FIG.

  Further, even if density or shift is mixed in the scanning line, the ideal scanning position after coordinate conversion can be obtained by using the equation (21) or the equation (22). The correction value setting unit 506 performs coordinate conversion of the ideal scanning position based on the positional deviation amount to obtain a correction value CnN, and outputs information of the correction value CnN to the filter coefficient setting unit 504.

(Filtering)
In the present embodiment, filter processing is performed to generate correction data. However, in the present embodiment, the filter processing unit 501 performs filter processing by convolution operation using the following filter function. That is, the filter processing unit 501 detects the pixel position in the sub scanning direction of the pixel by correcting the scanning position in the sub scanning direction of the pixel of the input image data and the pixel in which the scanning line interval is uniformly converted by coordinate conversion. Filtering is performed based on the positional relationship with the sub-scanning position. A pixel before filter processing is also called an input pixel, and a pixel after filter processing is also called an output pixel. Further, the pixel before the filtering process is a pixel on which the above-described coordinate conversion has been performed.

  The convolution function of this embodiment can be selected from linear interpolation shown in FIG. 13 (a) and bicubic interpolation shown in FIGS. 13 (b) and 13 (c). The filter function output unit 505 outputs, to the filter coefficient setting unit 504, information of a convolution function used for filter processing, for example, as information of a table. In FIG. 13, the vertical axis y indicates the position in the sub scanning direction, the unit is indicated by pixels, and the horizontal axis k indicates the magnitude of the coefficient. Although the unit of the vertical axis y is a pixel, it may be a line as it indicates the sub scanning direction.

図１３（ｂ）、図１３（ｃ）の式は以下の２つの式で表される。

本実施例では、ａ＝−１、図１３（ｂ）はｗ＝１、図１３（ｃ）はｗ＝１．５としているが、各画像形成装置の電子写真的な特性に応じて、ａ、ｗを調整してもよい。フィルタ係数設定部５０４は、フィルタ関数出力部５０５から得たフィルタ関数の情報と、補正値設定部５０６から出力された補正値Ｃの情報と、に基づいて、フィルタ処理に用いられる係数（後述するｋ）をフィルタ処理部５０１に出力する。 The equation of FIG. 13 (a) is expressed as follows.

The equations in FIG. 13B and FIG. 13C are expressed by the following two equations.

In this embodiment, although a = −1, FIG. 13B shows w = 1, and FIG. 13C shows w = 1.5, according to the electrophotographic characteristics of each image forming apparatus, a , W may be adjusted. The filter coefficient setting unit 504 uses coefficients (described later) based on the information on the filter function obtained from the filter function output unit 505 and the information on the correction value C output from the correction value setting unit 506 (described later. k) is output to the filter processing unit 501.

  Here, it demonstrates using FIG.13 (d). In FIG. 13D, the horizontal axis indicates the coefficient k used for the filtering process, and the vertical axis indicates the position y in the sub scanning direction. When the correction value CnN is input from the correction value setting unit 506, the filter processing unit 501 uses the filter function input from the filter function output unit 505 to obtain a coefficient kn corresponding to the correction value CnN. White circles in FIG. 13D indicate coefficients before coordinate conversion. Further, FIG. 13D shows that the coefficient k1 is set for the correction value C1N and the coefficient k2 is set for the correction value C2N as a coefficient kn used for the filtering process (black circle). In the present embodiment, the density per predetermined area of the input image data is stored by applying the same convolution function and sampling according to the ideal scanning position regardless of the density state of the input image data. It is like that.

(Specific example of filter processing)
Based on the coordinate position after performing the coordinate conversion of a present Example, the specific example which performs the filter processing using a convolution calculation with the filter function by linear interpolation of Formula (27) is demonstrated using FIG. The filter processing using the convolution operation is executed by the filter processing unit 501. FIG. 14 corresponds to FIG. The left column in FIG. 14 shows input pixels after the above-described coordinate conversion. The right column in FIG. 14 indicates the scanning position on the photosensitive drum 102 after the above-described coordinate conversion. That is, the scanning positions of the right-hand column in FIG. 14 are coordinate-transformed so as to have a distance of 1 at equal intervals.

  More specifically, the scanning position in the sub-scanning direction of the input pixel after coordinate conversion is the straight line indicated by the alternate long and short dash line in the graph after coordinate conversion shown on the right side of FIGS. 10 and 12 (y ′ = fs ′ (n)) Is represented by The scanning position on the photosensitive drum 102 after coordinate conversion is represented by a straight line (y '= ft' (n)) indicated by a solid line in the graph after coordinate conversion shown on the right side of FIGS. For example, in FIG. 10A, since the shift amount is +0.2 (= S), after coordinate conversion, fs' (n) = y-0.2 = n-0.2.

  Further, in FIG. 14, the magnitude of the pixel value, that is, the density value is indicated by the shade of a circle. Also, the numbers in parentheses are the numbers of scanning lines, which are the same as the pixel numbers described in FIG. In the central graph of FIG. 14, the horizontal axis indicates the density, and the vertical axis indicates the position in the sub-scanning direction. A convolution operation develops a waveform W (W1 to W5 for pixels (1) to (5)) obtained by multiplying a filter function (FIG. 13 (a)) centered on each coordinate position of the input pixel and overlapping. In addition, it is what was added.

  This will be described in order from FIG. 14 (a). Pixels (1) and (5) indicated by white circles have a density of 0, that is, a pixel value of 0. Therefore, W obtained by multiplying the filter function by the pixel value is W1 = 0 and W5 = 0. The densities of the pixels (2), (3), and (4) shown by black circles are equal, the maximum values of the waveforms of W2, W3, and W4 are equal, and the waveform is an expanded filter function centered on the pixel position of the input pixel. . The result of the convolution operation is the sum of all waveforms (ΣW n, n = 1 to 5).

  The pixel value of the output pixel is sampled at the scanning position on the photosensitive drum 102 after coordinate conversion of the scanning position. Therefore, for example, the pixel value (1) corresponding to the scanning position on the photosensitive drum 102 intersects with the waveform W2 at the point P0, and is thus calculated as the density D1. Further, since the pixel value (2) intersects the waveform W2 and the point P2 and the waveform W3 and the point P1 respectively, the pixel value (2) is calculated as the density D1 + D2. Hereinafter, pixel values (3) to (5) are similarly calculated. Since the pixel value (5) does not intersect with any waveform, the pixel value is set to 0. Moreover, the result of having calculated the pixel value of (1)-(5) of FIG.14 (b)-FIG.14 (d) is shown by the lightness and darkness of the pixel of each right column.

  The positional deviation of the input pixel is shown corresponding to each pixel on the vertical axis in FIG. The positional deviation amount shown on the vertical axis of FIG. 14 is information on the positional deviation amount obtained by the inverse function in accordance with the coordinate conversion of the scanning position of the pixel of the input image described above in the sub scanning direction. For example, in the case of FIG. 14A, as described in FIG. 10A, the correction amount C of the positional deviation amount S of the scanning line is −0.2. Further, for example, FIG. 14C shows the correction amount C calculated using the equation (25), and FIG. 14D using the equation (26).

  In FIG. 14A, the scanning position of the scanning line is shifted in the advancing direction in the sub-scanning direction, but the center of gravity is shifted in the opposite delay direction in the pixel value. It shows how it is. In FIG. 14B, the scanning position of the scanning line is shifted in the return direction in the sub-scanning direction, but the center of gravity is shifted in the backward direction of the pixel value, so the position of the center of gravity of the pixel value is corrected. It shows how it is. FIG. 14C shows the case where the scanning positions are closely spaced, the distribution of density spreads by convolution after coordinate conversion, and local concentration change is canceled to correct local density change. It shows the situation. Also, in FIG. 14D, when the scanning position interval is sparse, the density distribution is reduced by the convolution operation after the coordinate conversion, and the density distribution is canceled to correct the local density change. Showing how In particular, the pixel value of (3) in FIG. 14D has a density of (100 + α)% that is higher than 100%.

(Filtering)
It returns to the explanation of FIG. In step S3604 in FIG. 8, the CPU 303 performs filter processing by the filter processing unit 501 based on the correction attribute information generated in step S3603. Specifically, the CPU 303 performs the convolution operation and the resampling on the input image described above. Here, the processing of S3604 executed by the CPU 303 will be described in detail with reference to the flowchart of FIG. When the filter processing by the filter processing unit 501 is started by the filter processing unit 501, the CPU 303 executes the processing of S3703 and subsequent steps. When the spread of the convolution function is L in S3703, the range ((yn-L) to (yn + L) of the width 2L of the sub-scanning position of the line yn (position yn) of the output image of interest Extract the lines of the input image contained in Here, L is defined outside the range of + L to -L of the convolution function as the minimum value at which the value of the convolution function becomes zero. For example, in the linear interpolation of FIG. 13 (a), L = 1, the bicubic interpolation of FIG. 13 (b) is L = 2, and the bicubic interpolation of FIG. 13 (c) is L = 3. Using the equation (22), ymin and ymax in the range ymin to ymax of the corresponding input image satisfy the following conditions.
ft- ¹ (ymin) = yn-L, ft- ¹ (ymax) = yn + L Formula (30)
By transforming equation (30), ymin and ymax can be obtained from the following equation (31).
ymin = ft (yn-L), ymax = ft (yn + L) (31)
Therefore, the lines of the input image extracted for the line yn of the output image of interest are all integer lines in the range of ymin to ymax.

Assuming that a line yn of the output image to be noticed and a line of the input image to be subjected to the convolution operation are ym, the distance d nm is expressed by the following equation (32).
dnm = yn-ft- ¹ (ym) (32)
Therefore, in step S3704, the CPU 303 causes the filter coefficient setting unit 504 to obtain the coefficient k nm as the convolution function g (y) according to the following equation.
knm = g (dnm) ... Formula (33)

ここで、式（３４）は、図１４に対応しており、図１４の左側の丸の濃さ（濃度）は、入力画素データＰｉｎ_ｍに対応し、図１４（ａ）のＤ１やＤ２は、ｋ_ｎｍ×Ｐｉｎ_ｍに対応し、図１４の右側の丸の濃さ（濃度）は、Ｐｏｕｔ_ｎに対応している。 In step S3707, the CPU 303 acquires pixel data of the position n in the subscanning direction of the input image extracted in step S3703 and the position N in the main scanning direction to be focused. Here, pixel data is set as input pixel data Pin _m . In step S3708, the CPU 303 performs a convolution operation by the filter processing unit 501, and ends the processing. More specifically, the filter processing unit 501, the corresponding coefficient knm determined in S 3704, the input pixel data Pin _m acquired by the product-sum operation at S3707, obtains the value Pout _n of the pixel of interest. The input pixel data Pin _m is the density of the target pixel before filter processing, and the value P out _n of the target pixel is output pixel data, which is the density of the target pixel after filter processing.

Here, equation (34) corresponds to FIG. 14, and the density (density) of the circle on the left side of FIG. 14 corresponds to the input pixel data Pin _m , and D1 and D2 in FIG. , K _nm × Pin _m, and the density (concentration) of the circle on the right side of FIG. 14 corresponds to Pout _n .

  As described above, in the present embodiment, distortion and density unevenness of the image due to the deviation of the irradiation position due to the dispersion of the multi-beam position and the mirror surface of the rotary polygon mirror 204 are corrected as follows. First, the pixel position of the input image is coordinate-transformed based on the profile of positional deviation in the sub-scanning direction of the input image. After that, by filtering and sampling, it is possible to cancel local density deviation such as positional deviation and banding while preserving the density of each input pixel, and obtain a good image. In this embodiment, it is possible to calculate the amount of positional deviation in the sub-scanning direction, taking into consideration the surface inclination of the rotary polygon mirror 204 which differs in the main scanning direction.

  As described above, according to the present embodiment, it is possible to correct image distortion and density unevenness caused by displacement amounts that differ for each position in the main scanning direction, and to obtain excellent image quality.

102 Photosensitive drum 104 Optical scanning device 201 Laser light source 204 Rotating polygon mirror 302 Memory 303 CPU

Claims (10)

A light source having a plurality of light emitting elements; a photosensitive member which is rotated in a first direction and on which a latent image is formed by the light beam emitted from the light source; and deflects the light beam emitted from the light source; And a deflection unit configured to move a spot of a light beam irradiated to a body in a second direction orthogonal to the first direction to form a scanning line.
Storing, in a storage unit, information on positional deviation in the first direction according to the second direction of the scanning line;
Converting the position of the pixel of the input image by performing coordinate conversion such that the distance between the scanning lines on the photosensitive member becomes a predetermined distance based on the information stored in the storage unit;
A filter processing step of calculating a pixel value of a pixel of an output image by performing a convolution operation on a pixel value of a pixel of the input image based on the position of the pixel of the input image after the coordinate conversion;
A correction method comprising:   In the storage step, a region scanned by the light beam in the second direction is divided into a predetermined number of blocks, and information regarding positional deviation in the first direction for each of the divided blocks is stored in the storage means. The correction method according to claim 1, characterized in that:   In the conversion step, using the value obtained by performing linear interpolation in the second direction on the information on the positional deviation for each block stored in the storage means, the position of the pixel of the input image before the coordinate conversion The correction method according to claim 2, wherein: Let fs (n) be a function that indicates the position of the nth pixel in the first direction of the input image.
Let ft (n) be a function indicating the position of the n-th pixel in the first direction of the output image,
Let fs' (n) be a function indicating the position of the n-th pixel in the first direction of the input image after the coordinate conversion,
When a function indicating the position of the n-th pixel in the first direction of the output image after the coordinate conversion is ft ′ (n),
In the conversion step, the position of the pixel of the input image after the coordinate conversion is calculated using an inverse function ft ⁻¹ (n) of the function ft (n),
fs '(n) = ft' (ft- ¹ (fs (n)))
The correction method according to any one of claims 1 to 3, characterized by: When the function fs (n) satisfies fs (n) = n and the function ft '(n) satisfies ft' (n) = n
In the conversion step, the pixel position of the input image after the coordinate conversion is
fs' (n) = ft- ¹ (n)
The correction method according to claim 4, characterized in that:   The correction method according to any one of claims 3 to 5, wherein in the filtering step, the convolution operation is performed using linear interpolation or bicubic interpolation. The pixel value is a density value,
The correction according to any one of claims 3 to 6, wherein in the filtering step, density values per predetermined area are stored before and after performing the convolution operation. Method. In the filtering process, when the width in the first direction of the non-zero range of the convolution function used for the convolution operation is 2L, the width of the 2L centered on the position yn of the predetermined pixel of the output image For the range ymin to ymax of pixels of the input image corresponding to the range:
ymin = ft (yn-L),
ymax = ft (yn + L)
The correction method according to claim 4 or 5, characterized in that: The deflection means is a rotary polygon mirror having a predetermined number of faces,
9. The information stored in the storage means includes information on variations in the angle of each surface with respect to the rotation axis of the rotary polygon mirror, according to any one of claims 1 to 8, Correction method described in section.   The correction method according to any one of claims 1 to 9, wherein the predetermined interval is determined according to the resolution of image formation by the image forming apparatus.

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